Answer:
The length of the other two sides are: 43.09 and 32.60
Step-by-step explanation:
Let the given side of the triangle be b(= 40), and the angles be;
A = [tex]72^{o}[/tex], B = [tex]62^{o}[/tex]and C = [tex]46^{o}[/tex].
Applying the Sine rule,
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]
So that,
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]
[tex]\frac{a}{Sin 72}[/tex] = [tex]\frac{40}{Sin62}[/tex]
a = [tex]\frac{0.9511*40}{0.8829}[/tex]
= 43.0898
a = 43.09
Also,
[tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{40}{Sin62}[/tex] = [tex]\frac{c}{Sin46}[/tex]
c = [tex]\frac{0.7193*40}{0.8829}[/tex]
= 32.5881
c = 32.60
The length of the other two sides are: 43.09 and 32.60
